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high reputation in philology had not mathematics attracted
him more strongly. Having seen that the boy had mathematical
genius, the teacher (Heinrich Bauer) let Jacobi work by himself
- after a prolonged tussle in which Jacobi rebelled at learning
mathematics by rote and by rule.
Young Jacobi's mathematical development was in some
respects curiously parallel to that of his greater rival Abel.
Jacobi also went to the masters; the works of Euler and
Lagrange taught him algebra and the calculus, and introduced
him to the theory of numbers. This earliest self-instruction was
to give Jacobi's first outstanding work - in elliptic functions -
its definite direction, for Euler, the master of ingenious devices,
found in Jacobi his brilliant successor. For sheer manipulative
ability in tangled algebra Euler and Jacobi have had no rival,
unless it be the Indian mathematical genius, Srinivasa Rama-
mijan, in our own century. Abel also could handle formulae
like a master when he wished, but his genius was more philo-
sophical, less formal than Jacobfs, Abel is closer to Gauss in
his insistence upon rigour than Jacobi was by nature - not that
Jacobi's work lacked rigour, for it did not, but its inspiration
appears to have been formalistic rather than rigoristic.
Abel was two years older than JacobL Unaware that Abel
had attacked the general quintic in 1820, Jacobi in the same
year attempted a solution, reducing the general quintic to the
forma*5  Itopx ~p and showing that the solution of this equa-
tion would follow from that of a certain equation of the tenth
degree. Although the attempt was abortive it taught Jacobi a
gieat deal of algebra and he ascribed considerable importance
to it as a step m his mathematical education. But it does not
seem to have occurred to him, as it did to Abel, that the general
quintfo might he unsolvable algebraically. This oversight, or
lack of imagination, or whatever we wish to call it, on Jacobi's
part is typical of the difference between him and Abel. Jacobi,
wbo had a magnificently objective mind and not a particle of
envy or jealousy in his generous nature, himself said of one of
Abel's masterpieces, 'It is above my praises as it is above my
own works.*
JaoobFs student days at Berlin lasted from April 1821 to